A prime number p is a natural number greater than 1 that has only two natural divisors: 1 and p itself. Any natural number n, such that n > 1, has a unique decomposition into prime factors, for instance 4 = 2 × 2, 5 = 5, 6 = 2 × 3.

Let sopf(n) denote the sum of the prime factors of a natural number n. For instance, sopf(4) = 2 + 2 = 4, sopf(5) = 5, and sopf(6) = 2 + 3 = 5.

If we take the result of this sum, we may compute again the sum of its prime factors, and repeat this ad nauseam. However, at some point, we always reach a fix-point, that is a number f such that f = sopf(f). For instance, starting from 8, sopf(8) = 2 + 2 + 2 = 6, then sopf(6) = 2 + 3 = 5, and sopf(5) = 5: applying repetitively sopf from 8 generates the sequence 8, 6, 5, 5, 5,... So, from the initial value 8, it takes 3 applications of sopf to discover that we have reached a fix-point.

Let lsopf(n) denote the number of applications of sopf from n that is required to discover that the fix-point has been reached. For instance, lsopf(8) = 3 and lsopf(4) = 1.

Your task is, given two natural numbers n and m (with n > 1 and m > 1), find the largest value the function lsopf takes in the interval between n and m.